precal: find height of semi-elliptical tunnel

caitfrawley66

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On a country road, the entrance to a tunnel is in the shape of a semi ellipse having a horizontal span of 30 feet (at ground level) and a height of 14 feet (at its highest point in the middle). Ben and Eileen Dover are driving their RV to Montana and must pass through the tunnel. The RV's width is 10 feet and its total height is 13 feet. Will Bill and Eileen make it to Montana to enter the Western Division U.S. Bass Fishing Chapmpionship? (Note: they may not deflate their tires)
 
Find the equation for your ellipse nd see if the RV will fit.

The road is 30' wide, therefore, 15' on either side of the y-axis(the major axis of the ellipse); it's 14' high in the center(the minor axis).

\(\displaystyle \L\\\frac{x^{2}}{15^{2}}+\frac{y^{2}}{14^{2}}=1\)

Check and see if it'll fit. You know its heighth and width.

ellipseqn7.gif
 
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